Question: Rewrite as a simplified fraction. ${1.6\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 162.2222...\\ 10x &= 16.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 146}$ ${x = \dfrac{146}{90}} $ ${x = \dfrac{73}{45}} \text{or} {1 \dfrac{28}{45}}$